Gaussian Belief-Propagation and GBP Messages: To estimate the state variables \(\mathbf {s}\) , we apply message-passing GBP algorithm [1]}. GBP operates on the factor graph \(\mathcal {G}\)  by exchanging messages between factor nodes and variable nodes in both directions. As a general rule, at any variable or factor node, an outgoing message on any edge is obtained as a function of incoming messages from all other edges, using the message calculation rules presented below. In general, the underlying factor graph describing joint state estimation and signal detection problem (Fig. REF ) will contain cycles, thus the resulting GBP will be iterative, which means that all nodes will iteratively repeat message updates on all of the outgoing edges according to a given message-passing schedule. We provide details on message-passing schedule, correctness and convergence of GBP on loopy graphs later in this section.
